Subgroup of abelian group not implies powering-invariant
This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., subgroup of abelian group) need not satisfy the second subgroup property (i.e., powering-invariant subgroup)
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Thus, our example must be an infinite subgroup of infinite index.
The simplest example is as follows: is the additive group of rational numbers and . In this case, is powered over all primes, but is not powered over any.